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If |x–1|<4, so:

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If |x–1|<4, so:  [#permalink]

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New post 24 Oct 2017, 04:10
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Question Stats:

26% (01:16) correct 74% (01:19) wrong based on 665 sessions

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If |x–1|<4, so:

(A) x > 3
(B) x ≤ 4
(C) -4< x < 4
(D) x > -4
(E) none of the above
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Re: If |x–1|<4, so:  [#permalink]

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New post 24 Oct 2017, 04:13
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Re: If |x–1|<4, so:  [#permalink]

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New post 24 Oct 2017, 04:24
Bunuel wrote:
vitorpteixeira wrote:
If |x–1|<4, so:

(A) x > 3
(B) x ≤ 4
(C) -4< x < 4
(D) x > -4
(E) none of the above


\(|x–1|<4\);

\(-4<x-1<4\);

\(-3<x<5\).

Any x from that range will be more than -4.

Answer: D.

P.S. What is the source of this question?





Bunnel,

First of all, thank you very much.

The source of this questions is a bank of questions that I received from a friend, whose his teacher gave to him.

I have huge doubts on inequalities topics.

As you explained above any value X>-4 can satisfy this.

What is the best approach to deal with this kind of questions? I solved -3<x<5, but I could not figure out, X>-4 because -3>-4 and do not satisfy the inequality.

Can you please help?

I have the same doubt on this question, below...

https://gmatclub.com/forum/if-z-2-4z-5- ... l#p1949237
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If |x–1|<4, so:  [#permalink]

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New post 24 Oct 2017, 04:27
1
2
vitorpteixeira wrote:
Bunuel wrote:
vitorpteixeira wrote:
If |x–1|<4, so:

(A) x > 3
(B) x ≤ 4
(C) -4< x < 4
(D) x > -4
(E) none of the above


\(|x–1|<4\);

\(-4<x-1<4\);

\(-3<x<5\).

Any x from that range will be more than -4.

Answer: D.

P.S. What is the source of this question?





Bunnel,

First of all, thank you very much.

The source of this questions is a bank of questions that I received from a friend, whose his teacher gave to him.

I have huge doubts on inequalities topics.

As you explained above any value X>-4 can satisfy this.

What is the best approach to deal with this kind of questions? I solved -3<x<5, but I could not figure out, X>-4 because -3>-4 and do not satisfy the inequality.

Can you please help?

I have the same doubt on this question, below...

https://gmatclub.com/forum/if-z-2-4z-5- ... l#p1949237


It's the other way around. We know that \(-3<x<5\). Any x from that range satisfy x > -4.


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Re: If |x–1|<4, so:  [#permalink]

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New post 25 Oct 2017, 10:40
Bunuel wrote:
If |x–1|<4, so:

(A) x > 3
(B) x ≤ 4
(C) -4< x < 4
(D) x > -4
(E) none of the above


\(|x–1|<4\);

\(-4<x-1<4\);

\(-3<x<5\).

Any x from that range will be more than -4.

Answer: D.

P.S. What is the source of this question?[/quote]



Hi, Bunuel
Just wanted to ask that since in this question it is not mentioned that x is an integer, by the range x>-4 it will include values greater than -3 also (say -3.8) but our range is from -3 to 5 so isnt this wrong????
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Re: If |x–1|<4, so:  [#permalink]

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New post 25 Oct 2017, 10:51
suramya26 wrote:
Hi, Bunuel
Just wanted to ask that since in this question it is not mentioned that x is an integer, by the range x>-4 it will include values greater than -3 also (say -3.8) but our range is from -3 to 5 so isnt this wrong????


I tried to explain this in the post above.

We know that \(-3<x<5\). Any x from that range satisfy x > -4.


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Re: If |x–1|<4, so:  [#permalink]

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New post 26 Oct 2017, 15:47
1
vitorpteixeira wrote:
If |x–1|<4, so:

(A) x > 3
(B) x ≤ 4
(C) -4< x < 4
(D) x > -4
(E) none of the above


We can solve the inequality when (x - 1) is positive and when it is negative.

When (x - 1) is positive:

x - 1 < 4

x < 5

When (x - 1) is negative:

-x + 1 < 4

-x < 3

x > -3

-3 < x < 5

Answer: D
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If |x–1|<4, so:  [#permalink]

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New post 26 Oct 2017, 17:53
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IMO Option D is the right answer.
|x-1|<4 means
-4<x-1<4
-3<x<5
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Re: If |x–1|<4, so:  [#permalink]

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New post 27 Oct 2017, 05:01
It's a tricky question, I think I've encountered a sort of this one in OG2017.
Key to solve it is to find the range from the answer choices that covers all possible values of x,here it is answer choice D.
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Re: If |x–1|<4, so:  [#permalink]

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New post 27 Oct 2017, 11:03
1
I can't understand why x>-4 is the correct answer.

Since we have -3<x<5 , -3 is out of the range and in x> -4 -3 is included in the number line.

Besides that, X>-4 we can have x=10, as an exemple, wich is not true since x<5.

Can someone help me with this points?

tks
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Re: If |x–1|<4, so:  [#permalink]

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New post 01 Nov 2017, 08:13
Bunuel wrote:
vitorpteixeira wrote:
If |x–1|<4, so:

(A) x > 3
(B) x ≤ 4
(C) -4< x < 4
(D) x > -4
(E) none of the above


\(|x–1|<4\);

\(-4<x-1<4\);

\(-3<x<5\).

Any x from that range will be more than -4.

Answer: D.

P.S. What is the source of this question?


Hi Bunuel, thanks for the explanation. I tend to approach this questions in the wrong way, trying to find an answer choice that matches with the range found through the inequalities. For instance, in this case I was looking for -3<x<5 (or something more restrictive, such as -2 < x < -5), which led me to pick answer E.

Given your explanation, I understand that I should look for that condition that holds for every x in the range...but I still have a huge doubt.
You say it is (D) x > -4 because any X from that range will be more than -4. Following your logic, wouldn't also B) x ≤ 4 be true? Our range is -3<x<5, which means that every x will be less or equal to 4.

Is there something I am not getting right?

Your help is super appreciated
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Re: If |x–1|<4, so:  [#permalink]

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New post 01 Nov 2017, 09:53
1
delid wrote:
Bunuel wrote:
vitorpteixeira wrote:
If |x–1|<4, so:

(A) x > 3
(B) x ≤ 4
(C) -4< x < 4
(D) x > -4
(E) none of the above


\(|x–1|<4\);

\(-4<x-1<4\);

\(-3<x<5\).

Any x from that range will be more than -4.

Answer: D.

P.S. What is the source of this question?


Hi Bunuel, thanks for the explanation. I tend to approach this questions in the wrong way, trying to find an answer choice that matches with the range found through the inequalities. For instance, in this case I was looking for -3<x<5 (or something more restrictive, such as -2 < x < -5), which led me to pick answer E.

Given your explanation, I understand that I should look for that condition that holds for every x in the range...but I still have a huge doubt.
You say it is (D) x > -4 because any X from that range will be more than -4. Following your logic, wouldn't also B) x ≤ 4 be true? Our range is -3<x<5, which means that every x will be less or equal to 4.

Is there something I am not getting right?

Your help is super appreciated


For \(-3<x<5\), (B) x ≤ 4 won't always be true. For example, x could be 4.5 (4.5 IS between -3 and 5) and in this case B is not true.
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: If |x–1|<4, so:  [#permalink]

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New post 04 Nov 2017, 04:02
|x–1|<4


−3<x<5

Any x from that range will be more than -4.

Answer: D.
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Re: If |x–1|<4, so:  [#permalink]

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New post 14 Jan 2018, 23:12
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Re: If |x–1|<4, so:  [#permalink]

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New post 26 Mar 2018, 15:50
Wouldn't this question be better off as a "which of the following must be true" question? Does the actual test do stuff like this?
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Re: If |x–1|<4, so: &nbs [#permalink] 26 Mar 2018, 15:50
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